解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=30$$ 和公比：$$r=1.6$$ 插入几何级数的公式：

$$a_1=30$$

$$a_2=a_1·r^{n-1}=30\cdot {1.6}^{2-1}=30\cdot {1.6}^1=30\cdot 1.6=48$$

$$a_3=a_1·r^{n-1}=30\cdot {1.6}^{3-1}=30\cdot {1.6}^2=30\cdot 2.5600000000000005=76.80000000000001$$

$$a_4=a_1·r^{n-1}=30\cdot {1.6}^{4-1}=30\cdot {1.6}^3=30\cdot 4.096000000000001=122.88000000000002$$

$$a_5=a_1·r^{n-1}=30\cdot {1.6}^{5-1}=30\cdot {1.6}^4=30\cdot 6.553600000000001=196.60800000000003$$

$$a_6=a_1·r^{n-1}=30\cdot {1.6}^{6-1}=30\cdot {1.6}^5=30\cdot 10.485760000000003=314.5728000000001$$

$$a_7=a_1·r^{n-1}=30\cdot {1.6}^{7-1}=30\cdot {1.6}^6=30\cdot 16.777216000000006=503.3164800000002$$

$$a_8=a_1·r^{n-1}=30\cdot {1.6}^{8-1}=30\cdot {1.6}^7=30\cdot 26.84354560000001=805.3063680000002$$

$$a_9=a_1·r^{n-1}=30\cdot {1.6}^{9-1}=30\cdot {1.6}^8=30\cdot 42.94967296000002=1288.4901888000006$$

$$a_{10}=a_1·r^{n-1}=30\cdot {1.6}^{10-1}=30\cdot {1.6}^9=30\cdot 68.71947673600003=2061.584302080001$$